Gardner's Relation
Gardner's relation, or Gardner's equation, named after Gerald H. F. Gardner and L. W. Gardner, is an empirically derived equation that relates seismic P-wave velocity to the bulk density of the lithology in which the wave travels. The equation reads: :\rho = \alpha V_p^ where \rho is bulk density given in g/cm3, V_p is P-wave velocity given in ft/s, and \alpha and \beta are empirically derived constants that depend on the geology. Gardner et al. proposed that one can obtain a good fit by taking \alpha = 0.23 and \beta = 0.25. Assuming this, the equation is reduced to: :\rho = 0.23 V_p^, where the unit of V_p is feet/s. If V_p is measured in m/s, \alpha = 0.31 and the equation is: :\rho = 0.31 V_p^. This equation is very popular in petroleum exploration because it can provide information about the lithology from interval velocities obtained from seismic data. The constants \alpha and \beta are usually calibrated from sonic and density Density (volumetric mass density ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Gardner Equation
The Gardner equation is an integrable nonlinear partial differential equation introduced by the mathematician Clifford Gardner in 1968 to generalize KdV equation and modified KdV equation. The Gardner equation has applications in hydrodynamics, plasma physics and quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ... : \frac-(6 \varepsilon^2 u^2 + 6u) \frac+\frac=0, where \varepsilon is an arbitrary real parameter. See also * Korteweg–de Vries equation Notes References * Nonlinear partial differential equations Integrable systems {{theoretical-physics-stub ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Gerald Gardner (mathematician)
Gerald Henry Frazier Gardner (March 2, 1926 – July 25, 2009) was an Irish-American mathematician, geophysicist and social activist whose statistical analysis led to the banning of classified advertising segregated by gender in a 1973 ruling by the Supreme Court of the United States in the case '' Pittsburgh Press Co. v. Pittsburgh Commission on Human Relations''. On a professional basis, he did early work on the use of monitoring seismological vibrations to identify deposits of natural gas that became industry standards. Early life and education Gardner was born on March 2, 1926, in Tullamore, Ireland, and attended Trinity College in Dublin, where he majored in physics and mathematics, graduating in 1948. He moved to the United States, earning a masters in 1949 in applied mathematics at the Carnegie Institute of Technology (later known as Carnegie Mellon University) in 1949 and a Ph.D. at Princeton University in mathematical physics in 1953.Weber, Bruce"Gerald Gardner, ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Seismic
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes (or generally, quakes) and the generation and propagation of elastic waves through planetary bodies. It also includes studies of the environmental effects of earthquakes such as tsunamis; other seismic sources such as volcanoes, plate tectonics, glaciers, rivers, oceanic microseisms, and the atmosphere; and artificial processes such as explosions. Paleoseismology is a related field that uses geology to infer information regarding past earthquakes. A recording of Earth's motion as a function of time, created by a seismograph is called a seismogram. A seismologist is a scientist who works in basic or applied seismology. History Scholarly interest in earthquakes can be traced back to antiquity. Early speculations on the natural causes of earthquakes were included in the writings of Thales of Miletus () ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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P-wave
A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at any affected location or at a seismograph. P waves may be transmitted through gases, liquids, or solids. Nomenclature The name ''P wave'' can stand for either pressure wave (as it is formed from alternating compressions and rarefactions) or primary wave (as it has high velocity and is therefore the first wave to be recorded by a seismograph). The name '' S wave'' represents another seismic wave propagation mode, standing for secondary or shear wave, a usually more destructive wave than the primary wave. Seismic waves in the Earth Primary and secondary waves are body waves that travel within the Earth. The motion and behavior of both P and S waves in the Earth are monitored to probe the interior structure of the Earth. Discontinuities ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Bulk Density
In materials science, bulk density, also called apparent density, is a material property defined as the mass of the many particles of the material divided by the bulk volume. Bulk volume is defined as the total volume the particles occupy, including particle's own volume, inter-particle void volume, and the particles' internal pore volume. Bulk density is useful for materials such as powders, granules, and other "divided" solids, especially used in reference to mineral components (soil, gravel), chemical substances, pharmaceutical ingredients, foodstuff, or any other masses of corpuscular or particulate matter ( particles). Bulk density is not the same as the ''particle density'', which is an intrinsic property of the solid and does not include the volume for voids between particles (see: density of non-compact materials). Bulk density is an extrinsic property of a material; it can change depending on how the material is handled. For example, a powder poured into a c ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Lithology
The lithology of a rock unit is a description of its physical characteristics visible at outcrop, in hand or core samples, or with low magnification microscopy. Physical characteristics include colour, texture, grain size, and composition. Lithology may refer to either a detailed description of these characteristics, or a summary of the gross physical character of a rock. Examples of lithologies in the second sense include sandstone, slate, basalt, or limestone. Lithology is the basis of subdividing rock sequences into individual lithostratigraphic units for the purposes of mapping and correlation between areas. In certain applications, such as site investigations, lithology is described using a standard terminology such as in the European geotechnical standard Eurocode 7. Rock type The naming of a lithology is based on the rock type. The three major rock types are igneous, sedimentary, and metamorphic. Igneous rocks are formed directly from magma, which is a mixture o ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Geology
Geology (). is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which they are composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth sciences, including hydrology. It is integrated with Earth system science and planetary science. Geology describes the structure of the Earth on and beneath its surface and the processes that have shaped that structure. Geologists study the mineralogical composition of rocks in order to get insight into their history of formation. Geology determines the relative ages of rocks found at a given location; geochemistry (a branch of geology) determines their absolute ages. By combining various petrological, crystallographic, and paleontological tools, geologists are able to chronicle the geological history of the Earth as a whole. One aspect is to demonstrate the age of the Earth. Geology provides evidence for plate tectonics, the ev ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Hydrocarbon Exploration
Hydrocarbon exploration (or oil and gas exploration) is the search by petroleum geologists and geophysicists for hydrocarbon deposits, particularly petroleum and natural gas, in the Earth's crust using petroleum geology. Exploration methods Visible surface features such as oil seeps, natural gas seeps, pockmarks (underwater craters caused by escaping gas) provide basic evidence of hydrocarbon generation (be it shallow or deep in the Earth). However, most exploration depends on highly sophisticated technology to detect and determine the extent of these deposits using exploration geophysics. Areas thought to contain hydrocarbons are initially subjected to a gravity survey, magnetic survey, passive seismic or regional seismic reflection surveys to detect large-scale features of the sub-surface geology. Features of interest (known as ''leads'') are subjected to more detailed seismic surveys which work on the principle of the time it takes for reflected sound waves to travel ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Sonic Logging
Sonic logging is a well logging tool that provides a formation’s interval transit time, designated as t, which is a measure of a how fast elastic seismic compressional and shear waves travel through the formations. Geologically, this capacity varies with many things including lithology and rock textures, most notably decreasing with an increasing effective porosity and increasing with an increasing effective confining stress. This means that a sonic log can be used to calculate the porosity, confining stress, or pore pressure of a formation if the seismic velocity of the rock matrix, V_, and pore fluid, V_l, are known, which is very useful for hydrocarbon exploration. Process of sonic logging The velocity is calculated by measuring the travel time from the piezoelectric transmitter to the receiver, normally with the units microsecond per foot (a measure of slowness). To compensate for the variations in the drilling mud thickness, there are actually two receivers, one nea ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Density Logging
Density logging is a well logging tool that can provide a continuous record of a formation's bulk density along the length of a borehole. In geology, bulk density is a function of the density of the minerals forming a rock (i.e. matrix) and the fluid enclosed in the pore spaces. This is one of three well logging tools that are commonly used to calculate porosity, the other two being sonic logging and neutron porosity logging History & Principle The tool was initially developed in the 1950s and became widely utilized across the hydrocarbon industry by the 1960s. A type of active nuclear tool, a radioactive source and detector are lowered down the borehole and the source emits medium-energy gamma rays into the formation. Radioactive sources are typically a directional Cs-137 source. These gamma rays interact with electrons in the formation and are scattered in an interaction known as Compton scattering. The number of scattered gamma rays that reach the detector, placed at a set ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |